Synthetic aperture radar (SAR) imaging of ocean waves is well understood, and valid physical models have been proposed to describe the forward mapping from ocean wave spectra to SAR image spectra. However, retrieving wave spectra from SAR spectra typically requires precise prior wave spectra, which impedes the further development of SAR-based ocean wave observations. The primary challenge lies in the fact that directly solving the inverse nonlinear mapping is mathematically infeasible due to azimuthal cutoff effects. This study developed a data-driven strategy to approximate the inverse nonlinear mapping without relying on prior information. A simulated SAR-Wave spectrum database was created based on the forward nonlinear mapping and then a deep learning model was trained on this database to approximate the inverse nonlinear mapping. Extensive evaluations on 79,371 retrieval wave spectra across weakly to strongly nonlinear SAR imaging regimes demonstrate the effectiveness of the approximated inverse nonlinear mapping. Under strongly nonlinear SAR imaging conditions, the rootmean-square errors are 0.27 m for significant wave height, 0.53 s for mean wave period, 35.78 m for peak wavelength, and 17.4 • for peak direction. Further testing on practical GF-3 SAR wave mode data shows that the SAR spectra reconstructed from the retrieved wave spectra align well with the observed SAR spectra, confirming the validity of the approximated inverse transformation. This work highlights the potential of integrating deep learning techniques with the SAR wave imaging theory to enable reliable and near-real-time SAR wave spectrum retrieval, thereby advancing the development of operational SAR ocean observation systems.